improved radiance gradient computation jaroslav křivánek pascal gautron kadi bouatouch sumanta...

Improved Radiance Gradient Computation

Jaroslav Křivánek

Pascal Gautron

Kadi Bouatouch

Sumanta Pattanaik

ComputerGraphicsGroup

Improved Radiance Gradient Computation2/35

Indirect lighting on glossy surfaces

With indirect Without indirect


Indirect lighting on glossy surfaces

With indirect Without indirect


Problem to solve Illumination integral evaluation at each visible

point

P

i),( ii PL

iiioiioo dBRDFPLPL cos),(),(),(

i


Brute Force Approach Monte Carlo gathering For each visible point

Slow convergence rate

Cast hundreds of rays


Slow Monte Carlo Convergence - Example 40 samples per pixel

Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/


Slow Monte Carlo Convergence – Example 1200 samples per pixel



Observation Indirect lighting on rough glossy surfaces is

rather smooth: abrupt changes are rare


Radiance Caching Approach Sparse sampling of indirect illumination Interpolation

Based on gradients


Radiance Caching

SceneRadiance

Cache

P1

Radiance cache lookup

CacheMiss!

Samplehemisphere

Project to hemispherical

harmonics

P1

Store incache

Lo=∫ x BRDF(P1) x cos θ dωLo(P1)

P2

Radiancecachelookup

Lo(P2)=∫ x BRDF(P2) x cos θ dωLo(P2)


ProblemReality

P1 P2

With radiance caching

P1 P2

Li(P1) = Li(P2)Li(P1) != Li(P2)

Wrong extrapolation


Wrong Extrapolation How does Li(P) change with P?

( Li(P) = incoming radiance at P )

First approximation = RADIANCE GRADIENT

Our contribution New radiance gradient computation


Wrong Extrapolation


Corrected with the New Gradients


Radiance Gradients: Problem Definition – Prerequisites Incoming radiance Li(P) representation

Li(P) is defined over a hemisphere Represented using hemispherical harmonics

Li(P) represented by a set of coefficients

),(),;(1

0

n

l

l

lm

ml

mli HPL

Coefficients

Basis functions


Radiance Gradients: Problem Definition – Prerequisites Coefficients computed with Monte Carlo

quadrature Uniform hemisphere

sampling Stratification

1

0

1

0,,, ),(

2 M

j

N

kkjkj

ml

ikj

ml HL

NM

Sum over all strata

Incoming radiance from the sampled direction

Multiplied by thebasis function


Radiance Gradients: Problem Definition Coefficients – hemisphere sampling

Gradients from the same hemisphere sampling Something like

1

0

1

0,,, ),(

2 M

j

N

kkjkj

ml

ikj

ml HL

NM

1

0

1

0, ......

M

j

N

k

ikj

ml L


Previous Work - Polygonal emitters

Arvo 1994 Irradiance Jacobian due to partially occluded

polygonal emitters of constant radiosity Holzschuch and Sillion 1995

Polygonal emitters of arbitrary radiosity


Previous Work - Hemisphere sampling Ward and Heckbert 1992 “Irradiance gradients”

Specifically for irradiance Cosine-proportional, uniformly weighted samples over

the hemisphere We extend this to uniformly distributed, arbitrarily

weighted samples Křivánek et al. 2005, Annen 2004

Radiance gradient Works mostly fine, except when there is occlusion in

the sampled environment We improve quality of this


Gradient Computation

1. Compute contribution from each hemisphere cell

2. Sum it all together


Gradient Computation for One Cell



Wall movement => cell area changes

Cell area change => solid angle changes

Solid angle change => incoming radiance changes


Putting it all together Sum incoming radiance changes from all cells Use the basis functions H as a weighting factor

Basis functions do not change with displacement

Cell area change

Incoming radiance change

Weighting by thebasis function


Results

Old gradients New gradients - smooth


Results

New gradientsOld gradients


Results

Old gradients


Results

New gradients


Gradients for GPU-based irradiance and radiance caching Hemisphere sampling = GPU rasterization Camera position = hemisphere center

Very non-uniform density of samples over the hemisphere

The same gradient derivation still holds (and WORKS!).

P


Gradients for GPU-based irradiance and radiance caching Irradiance caching video Offline irradiance caching video Radiance caching video – castle, walt disney

hall


Conclusion New translational gradient computation Use information from hemisphere sampling Based on the Irradiance Gradients by Ward and

Heckbert Generalized to support

Arbitrary distribution of radiance samples over the hemisphere

Arbitrary weighting of radiance samples


Thank you

? ?

improved radiance gradient computation jaroslav křivánek pascal gautron kadi bouatouch sumanta...

Documents

radiance gradient works

strata incoming radiance

cell slide

rare slide

radiance caching p1p1

indirectwithout indirect

basis function slide

wrong extrapolation